Beginning Math and Physics for Game Programmers

Properties of Lines

Now that we've defined the equation of a line, let's look at its properties a little more closely. One of the most important elements of a line is its slope, or steepness. Figure 1.12 shows a hill (a straight line) that rises steadily at a rate of 50m of vertical “rise” for each 100m of horizontal “run.”

Figure 1.12. A hill represented by a straight line.

The steepness of this incline is measured by the ratio of its rise to its run, which in this case is 50/100, or 50%. This same hill can be mathematically represented by the linear equation ½x – y = c, as shown in Figure 1.13.

Figure 1.13. Line ½x – y = c with slope ½.

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